Review of Fundamentals 1
We relate frequency and wavelength by: c=λ/ν
where c = speed of light (a constant), λ = wavelength and v =
frequency.
As wavelength increases, both frequency and energy content
decrease.
IMPORTANCE to remote sensing:
Less energy at longer wavelengths means:
we have to “sense” large areas to have sufficient energy to
produce good signal-to-noise ratio.
( i.e., low spatial resolution)
As a result,
• in the visible region, we can sense areas <1m2
• in the microwave bands, we sense areas >1km2
Review of Fundamentals 2
The relationship of quanta energy and
wavelength is characterized by
Q = hν
Where Q is energy (J), h is Planck’s constant
(6.6260 x 10-34 J s),
and ν is the frequency (c/λ).
Problem:
Calculate the wavelength of a quantum of radiation
whose photon energy is 2.10 x 10-19 Joules; use 3 x
108 m/sec as the speed of light ?
Problem:
Calculate the wavelength of a quantum of radiation
whose photon energy is 2.10 x 10-19 Joules; use 3 x
108 m/sec as the speed of light ?
The appropriate equation is:
Q = hν = h(c/λ), or
λ(in meters) = hc/Q.
Thus,
h
c
/
λ
Wavelength = (6.626 x 10-34) (3.00 x 108)/(2.10 x 10-19)
= 9.4657 x 10-7m
• radio waves
• visible
• ultraviolet
• x-rays
• gamma rays
1 x 108 Hz
4 x 1014 Hz
7.5 x 1016 Hz
3 x 1017 Hz
3 x 1018 Hz
1 MegaHertz is million cycles per second.
Example Problem
• A radio station broadcasts at 120 MHz;
what is the corresponding wavelength
in meters?
• A radio station broadcasts at 120 MHz;
what is the corresponding wavelength
in meters?
The equation is:
λ = c/ν
Thus,
λ = (3.00 x 108) / (120 x 106) = 0.02439 x 102
» = 2.5 meters
EMR Spectrum
Gamma rays and x-rays (normally measured in Å) < 10 Å; Earth’s atmosphere
blocks this radiation almost completely.
Ultraviolet 1-400 nm; Most blocked by Earth’s atmosphere (O3 absorption)
except from 300-400 nm.
Visible 400-700 nm; peak solar wavelengths; Earth’s atmosphere almost
completely transparent (relatively speaking to other EMR).
Reflective (near) infrared 700-3000 nm (0.7 – 3.0 μm); photography limited to
0.7-0.9 μm called photographic IR; high absorption by water vapor in the
atmosphere.
Thermal (far) infrared 3.0 – 10,000 μm; terrestrially derived; absorption by
water vapor and CO2 in atmosphere.
Microwave – 0.1 – 30 cm; wavelengths used in RADAR; atmosphere mostly
transparent
Radio - > 30 cm; classified RADARS; atmosphere almost completely
transparent.
Terminology
Radiant Energy (J)
Add time
Hemispherical
Radiant Flux (J/s) Φ
add area
Directional
add direction
Radiant Flux Density (W/m²)
Radiant Intensity (W/sr) I
Irradiance (incident)
Radiant Exitance (emitted)
Radiance (W/m²/sr) L
M
add wavelength
Radiant Spectral Flux Density (W/m²/μm)
add wavelength
Spectral Radiance (W/m²/sr/μm)
Most sensors yield these values
Lλ
Consider a 60 W light bulb. An electric current passes through the tungsten filament
and heats it to ~3000°K. Our bulb is perfect in the sense that it radiates all of this
energy, perhaps as a gray
body.
M
R
dΩ
E
θ
L
radiant flux (total)
radiant intensity
radiant exitance
radiance (brightness temp.)
irradiance
Φ
I
M
L
E
d Φ /dΩ
d Φ /dA
cosθ d2 Φ /(dΩdA)
d Φ /dA
60 W
60/4π W sr-1
60/4πR2 W m-2
W sr-1 m-2
W m-2
Wein’s Law:
Planck’s Law:
2 Forms of Planck’s Radiation Law
T -temperature
c -speed of light = 2.99 x 10-8 m s-1
h -Planck's constant = 6.63 x 10-34 J s
k -Boltzmann's constant = 1.38x10-23 J K-1
Lλ -spectral radiance = W m-3 sr -1
Lν -spectral radiance = W m-2 Hz-1 sr -1
Lλ
Lν